Resonant tunneling through a macroscopic charge state in a superconducting SET transistor

We predict theoretically and observe in experiment that the differential conductance of a superconducting SET transistor exhibits a peak which is a complete analogue in a macroscopic system of a standard resonant tunneling peak associated with tunneling through a single quantum state. In particular, in a symmetric transistor, the peak height is universal and equal to $e^2/2\pi \hbar$. Away from the resonance we clearly observe the co-tunneling current which in contrast to the normal-metal transistor varies linearly with the bias voltage.Comment: 11 pages, 3 figures, Fig. 1 available upon request from the first autho

Scattering Theory of Mesoscopic Detectors

We consider a two-level system coupled to a mesoscopic two-terminal conductor that acts as measuring device. As a convenient description of the conductor we introduce its scattering matrix. We show how its elements can be used to calculate the relaxation and decoherence rates of the two-level system. Special emphasis is laid on the charge screening in the conductor that becomes important in the many-channel limit. Finally we give some examples that illustrate charge screening in different limits.Comment: contribution to the ECOSS-21 proceedings in a special issue of SURFACE SCIENC

Method for direct observation of coherent quantum oscillations in a superconducting phase qubit

Time-domain observations of coherent oscillations between quantum states in mesoscopic superconducting systems were so far restricted to restoring the time-dependent probability distribution from the readout statistics. We propose a new method for direct observation of Rabi oscillations in a phase qubit. The external source, typically in GHz range, induces transitions between the qubit levels. The resulting Rabi oscillations of supercurrent in the qubit loop are detected by a high quality resonant tank circuit, inductively coupled to the phase qubit. Detailed calculation for zero and non-zero temperature are made for the case of persistent current qubit. According to the estimates for dephasing and relaxation times, the effect can be detected using conventional rf circuitry, with Rabi frequency in MHz range.Comment: 5 pages, 1 figure, to appear in Phys.Rev.

Shot noise for resonant Cooper pair tunneling

We study intrinsic noise of current in a superconducting single-electron transistor, taking into account both coherence effects and Coulomb interaction near a Cooper-pair resonance. Due to this interplay, the statistics of tunneling events deviates from the Poisson distribution and, more important, it shows even-odd asymmetry in the transmitted charge. The zero-frequency noise is suppressed significantly when the quasiparticle tunneling rates are comparable to the coherent oscillation frequency of Cooper pairs.Comment: A few minor changes; To appear in Phys. Rev. Let

Charge and current fluctuations in a superconducting single electron transistor near a Cooper pair resonance

We analyze charge tunneling statistics and current noise in a superconducting single-electron transistor in a regime where the Josephson-quasiparticle cycle is the dominant mechanism of transport. Due to the interplay between Coulomb blockade and Josephson coherence, the probability distribution for tunneling events strongly deviates from a Poissonian and displays a pronounced even--odd asymmetry in the number of transmitted charges. The interplay between charging and coherence is reflected also in the zero-frequency current noise which is significantly quenched when the quasi-particle tunneling rates are comparable to the coherent Cooper-pair oscillation frequency. Furthermore the finite frequency spectrum shows a strong enhancement near the resonant transition frequency for Josephson tunneling.Comment: 10 pages, 11 figure

Resonant Tunneling through Linear Arrays of Quantum Dots

We theoretically investigate resonant tunneling through a linear array of quantum dots with subsequent tunnel coupling. We consider two limiting cases: (i) strong Coulomb blockade, where only one extra electron can be present in the array (ii) limit of almost non-interacting electrons. We develop a density matrix description that incorporates the coupling of the dots to reservoirs. We analyze in detail the dependence of the stationary current on the electron energies, tunnel matrix elements and rates, and on the number of dots. We describe interaction and localization effects on the resonant current. We analyze the applicability of the approximation of independent conduction channels. We find that this approximation is not valid when at least one of the tunnel rates to the leads is comparable to the energy splitting of the states in the array. In this case the interference of conduction processes through different channels suppresses the current.Comment: 12 pages, 5 figure

Quantum Dynamics in Non-equilibrium Strongly Correlated Environments

We consider a quantum point contact between two Luttinger liquids coupled to a mechanical system (oscillator). For non-vanishing bias, we find an effective oscillator temperature that depends on the Luttinger parameter. A generalized fluctuation-dissipation relation connects the decoherence and dissipation of the oscillator to the current-voltage characteristics of the device. Via a spectral representation, this result is generalized to arbitrary leads in a weak tunneling regime.Comment: 4 pages, 1 figur

Theory of weak continuous measurements in a strongly driven quantum bit

Continuous spectroscopic measurements of a strongly driven superconducting qubit by means of a high-quality tank circuit (a linear detector) are under study. Output functions of the detector, namely, a spectrum of voltage fluctuations and an impedance, are expressed in terms of the qubit spectrum and magnetic susceptibility. The nonequilibrium spectrum of the current fluctuations in the qubit loop and the linear response function of the driven qubit coupled to a heat bath are calculated with Bloch-Redfield and rotating wave approximations. Backaction effects of the qubit on the tank and the tank on the qubit are analyzed quantitatively. We show that the voltage spectrum of the tank provides detailed information about a frequency and a decay rate of Rabi oscillations in the qubit. It is found that both an efficiency of spectroscopic measurement and measurement-induced decoherence of the qubit demonstrate a resonant behaviour as the Rabi frequency approaches the resonant frequency of the tank. We determine conditions when the spectroscopic observation of the Rabi oscillations in the flux qubit with the tank circuit can be considered as a weak continuous quantum measurement.Comment: 28 page

Selective quantum evolution of a qubit state due to continuous measurement

We consider a two-level quantum system (qubit) which is continuously measured by a detector. The information provided by the detector is taken into account to describe the evolution during a particular realization of measurement process. We discuss the Bayesian formalism for such ``selective'' evolution of an individual qubit and apply it to several solid-state setups. In particular, we show how to suppress the qubit decoherence using continuous measurement and the feedback loop.Comment: 15 pages (including 9 figures